Typically the random variables lie in a unital algebraA such as a C-star algebra or a von Neumann algebra. The algebra comes equipped with a noncommutative expectation, a linear functional φ: A → C such that φ(1) = 1. Unital subalgebras A1, ..., Am are then said to be freely independent if the expectation of the product a1...an is zero whenever each aj has zero expectation, lies in an Ak, and no adjacent aj's come from the same subalgebra Ak. Random variables are freely independent if they generate freely independent unital subalgebras.